Non-Abelian Vortices on Riemann Surfaces: an Integrable Case

We consider U(n + 1) Yang–Mills instantons on the space Σ × S ², where Σ is a compact Riemann surface of genus g. Using an SU(2)-equivariant dimensional reduction, we show that the U(n + 1) instanton equations on Σ × S ² are equivalent to non-Abelian vortex equations on Σ. Solutions to these equations are given by pairs (A,?), where A is a gauge potential of the group U(n) and ? is a Higgs field in the fundamental representation of the group U(n). We briefly compare this model with other non-Abelian Higgs models considered recently. Afterwards we show that for g > 1, when Σ × S ² becomes a gravitational instanton, the non-Abelian vortex equations are the compatibility conditions of two linear equations (Lax pair) and therefore the standard methods of integrable systems can be applied for constructing their solutions.     

ΛN and ΣN Interactions from Lattice QCD

We present our recent study on ΛN and ΣN (isospin I = 3/2) interactions by measuring Nambu–Bethe–Salpeter wave functions on the Lattice QCD. The lattice QCD calculation is performed by using the N _f  = 2 + 1 gauge configurations generated by PACS-CS collaboration together with employing an improved method to obtain potentials in lattice QCD simulations. For the ¹ S ₀ channel, the central ΣN (I = 3/2) potential and the central ΛN (¹ S ₀) potential are found to be very similar. For the spin triplet (³ S ₁?³ D ₁) channels, the central ΛN(³ S ₁?³ D ₁) potential is attractive while the central ΣN(I = 3/2, ³ S ₁?³ D ₁) potentials is repulsive. Tensor potentials, on the other hand, are rather weak in both ΛN and ΣN(I = 3/2) systems.     

On the Absence of Ferromagnetism in Typical 2D Ferromagnets

We consider the Ising systems in d dimensions with nearest-neighbor ferromagnetic interactions and long-range repulsive (antiferromagnetic) interactions that decay with power s of the distance. The physical context of such models is discussed; primarily this is d = 2 and s = 3 where, at long distances, genuine magnetic interactions between genuine magnetic dipoles are of this form. We prove that when the power of decay lies above d and does not exceed d + 1, then for all temperatures the spontaneous magnetization is zero. In contrast, we also show that for powers exceeding d + 1 (with d ≥ 2) magnetic order can occur.     

EPR and Optical Absorption Study of Cu2+-Doped Diammonium Hexaaqua Magnesium Sulphate Single Crystals

Electron paramagnetic resonance (EPR) study of Cu²⁺ ions doped in diammonium hexaaqua magnesium sulphate single crystal over the temperature range of 4.2–320 K is reported. Copper enters the lattice substitutionally and is trapped at two magnetically equivalent sites. The spin Hamiltonian parameters are evaluated at 320, 300, 77, and 4.2 K. The angular variations of the resonance lines in three mutually perpendicular planes ab, bc* and c*a are used to determine principal g and A values. The observed spectra are fitted to a spin Hamiltonian of rhombic symmetry with parameters of Cu²⁺ at 77 and 4.2 K: g _xx  = 2.089, g _yy  = 2.112, g _zz  = 2.437 (±0.002) and A _xx  = 38, A _yy  = 14, A _zz  = 110 (±2) × 10^?4 cm^?1. The ground state wave function of Cu²⁺ ion in this lattice is determined. The g-factor anisotropy is calculated and compared with the experimental value. The optical absorption spectra of the crystal are also recorded at room temperature. With the help of assigned bands the crystal-field parameters (Dq, Ds and Dt) are evaluated. By correlating the optical and EPR data, the nature of bonding in the complex is discussed. The temperature dependence of the g values is explained to conclude the occurrence of both static and dynamic Jahn–Teller effects over the temperature range of investigation.     

Bound States of Energy Dependent Singular Potentials

We consider attractive power-law potentials depending on energy through their coupling constant. These potentials are proportional to 1/|x| ^m with m ≥ 1 in the D = 1 dimensional space, to 1/r ^m with m ≥ 2 in the D = 3 dimensional space. We study the ground state of such potentials. First, we show that all singular attractive potentials with an energy dependent coupling constant are bounded from below, contrarily to the usual case. In D = 1, a bound state of finite energy is found with a kind of universality for the eigenvalue and the eigenfunction, which become independent on m for m > 1. We prove the solution to be unique. A similar situation arises for D = 3 for m > 2, except that, in this case, the solution is not directly comparable to a bound state: the wave function, though square integrable, diverges at the origin.     

Electron Paramagnetic Resonance and Electron Spin Echo Studies of Co2+ Coordination by Nicotinamide Adenine Dinucleotide (NAD+) in Water Solution

Co²⁺ binding to the nicotinamide adenine dinucleotide (NAD⁺) molecule in water solution was studied by electron paramagnetic resonance (EPR) and electron spin echo at low temperatures. Cobalt is coordinated by NAD⁺ when the metal is in excess only, but even in such conditions, the Co/NAD⁺ complexes coexist with Co(H₂O)₆ complexes. EPR spin-Hamiltonian parameters of the Co/NAD⁺ complex at 6 K are g _z  = 2.01, g _x  = 2.38, g _y  = 3.06, A _z  = 94 × 10^?4 cm^?1, A _x  = 33 × 10^?4 cm^?1 and A _y  = 71 × 10^?4 cm^?1. They indicate the low-spin Co²⁺ configuration with S = 1/2. Electron spin echo envelope modulation spectroscopy with Fourier transform of the modulated spin echo decay shows a strong coordination by nitrogen atoms and excludes the coordination by phosphate and/or amide groups. Thus, Co²⁺ ion is coordinated in pseudo-tetrahedral geometry by four nitrogen atoms of adenine rings of two NAD⁺ molecules.     

Observation of the v′=8←v=0 vibrational overtone in cold trapped HD+

We report the observation of the hitherto undetected v′=8←v=0 vibrational overtone in trapped HD⁺ molecular ions, sympathetically cooled by laser-cooled Be⁺ ions. The overtone is excited using 782 nm laser radiation, after which HD⁺ ions in v=8 are photodissociated by the 313 nm laser used for Be⁺ cooling. The concomitant loss of HD⁺ is detected by the method of secular excitation (Roth et al. in Phys. Rev. A. 74:040501(R), 2006). We furthermore present details of the experimental setup, and we show that results from spectroscopy of v′=8←v=0 overtones in combination with accurate ab initio calculations may yield a new value for the proton–electron mass ratio with an accuracy of order 1 ppb.     

Non-Intersecting Squared Bessel Paths at a Hard-Edge Tacnode

The squared Bessel process is a 1-dimensional diffusion process related to the squared norm of a higher dimensional Brownian motion. We study a model of n non-intersecting squared Bessel paths, with all paths starting at the same point a > 0 at time t = 0 and ending at the same point b > 0 at time t = 1. Our interest lies in the critical regime ab = 1/4, for which the paths are tangent to the hard edge at the origin at a critical time ${t^*\in (0,1)}$ . The critical behavior of the paths for n → ∞ is studied in a scaling limit with time t = t ^* + O(n ^?1/3) and temperature T = 1 + O(n ^?2/3). This leads to a critical correlation kernel that is defined via a new Riemann-Hilbert problem of size 4 × 4. The Riemann-Hilbert problem gives rise to a new Lax pair representation for the Hastings-McLeod solution to the inhomogeneous Painlevé II equation q′′(x) = xq(x) + 2q ³(x) ? ν, where ν = α + 1/2 with α > ?1 the parameter of the squared Bessel process. These results extend our recent work with Kuijlaars and Zhang (Comm Pure Appl Math 64:1305–1383, 2011) for the homogeneous case ν = 0.     

High-field EPR Study of the Effect of Chloride on Mn2+ Ions in Frozen Aqueous Solutions

The effect of chloride concentration on Mn²⁺ (S = 5/2, I = 5/2) ions in frozen aqueous solutions is studied by high-field high-frequency electron paramagnetic resonance (HFEPR). The usually six sharp lines characteristic of Mn²⁺ ions, arising from the m _s  = ?1/2 → 1/2 transition, is modified by the addition of Cl^? anions and the six resonances become much broader and more complex. This new feature likely arises from the ligation of one Cl^? anion to a hydrated Mn²⁺ ion forming a [Mn(H₂O)₅Cl]^? complex. This complex increases linearly with Cl^? concentration with an association constant of K _{a, apparent} = 61 M^?1. The structure of the putative chloride complex was studied using density functional theory calculations and the expected zero-field interaction of such a manganese center was calculated using the superposition model. The predicted values were similar to those determined from the simulation of the spectrum of the m _s  = ?5/3 → ?3/2 transition of the chloride complex. This effect of Cl^? anions occurs at biologically relevant concentration and can be used to probe the Mn²⁺ ions in cellular and protein environments.     

Time Scale Separation and Dynamic Heterogeneity in the Low Temperature East Model

We consider the non-equilibrium dynamics of the East model, a linear chain of 0–1 spins evolving under a simple Glauber dynamics in the presence of a kinetic constraint which forbids flips of those spins whose left neighbor is 1. We focus on the glassy effects caused by the kinetic constraint as ${q\downarrow 0}$ , where q is the equilibrium density of the 0s. In the physical literature this limit is equivalent to the zero temperature limit. We first prove that, for any given L = O(1/q), the divergence as ${q\downarrow 0}$ of three basic characteristic time scales of the East process of length L is the same. Then we examine the problem of dynamic heterogeneity, i.e., non-trivial spatio-temporal fluctuations of the local relaxation to equilibrium, one of the central aspects of glassy dynamics. For any mesoscopic length scale L = O(q ^?γ ), γ < 1, we show that the characteristic time scale of two East processes of length L and λ L respectively are indeed separated by a factor q ^?α , α = α(γ) > 0, provided that λ ≥ 2 is large enough (independent of q, λ = 2 for γ < 1/2). In particular, the evolution of mesoscopic domains, i.e., maximal blocks of the form 111..10, occurs on a time scale which depends sharply on the size of the domain, a clear signature of dynamic heterogeneity. A key result for this part is a very precise computation of the relaxation time of the chain as a function of (q, L), well beyond the current knowledge, which uses induction on length scales on one hand and a novel algorithmic lower bound on the other. Finally we show that no form of time scale separation occurs for γ = 1, i.e., at the equilibrium scale L = 1/q, contrary to what was assumed in the physical literature based on numerical simulations.     

Efimov Spectrum in Bosonic Systems with Increasing Number of Particles

It is well-known that three-boson systems show the Efimov effect when the two-body scattering length a is large with respect to the range of the two-body interaction. This effect is a manifestation of a discrete scaling invariance (DSI). In this work we study DSI in the N-body system by analysing the spectrum of N identical bosons obtained with a pairwise gaussian interaction close to the unitary limit. We consider different universal ratios such as \({E_N^0/E_3^0}\) and \({E_N^1/E_N^0}\) , with \({E_N^i}\) being the energy of the ground (i = 0) and first-excited (i = 1) state of the system, for \({N \leq16}\) . We discuss the extension of the Efimov radial law, derived by Efimov for N = 3, to general N.     

EPR and Optical Absorption Study of Cr3+-Doped Dipotassium Tetrachloropalladate

X-band electron paramagnetic resonance (EPR) study of Cr³⁺-doped dipotassium tetrachloropalladate single crystal is done at liquid nitrogen temperature. EPR spectrum shows two sites. The spin-Hamiltonian parameters have been evaluated by employing hyperfine resonance lines observed in EPR spectra for different orientations of crystal in externally applied magnetic field. The values of spin-Hamiltonian and zero-field splitting (ZFS) parameters of Cr³⁺ ion-doped DTP for site I are: g _x  = 2.096 ± 0.002, g _y  = 2.167 ± 0.002, g _z  = 2.220 ± 0.002, D = (89 ± 2) × 10^?4 cm^?1, E = (16 ± 2) × 10^?4 cm^?1. EPR study indicates that Cr³⁺ ion enters the host lattice substitutionally replacing K⁺ ion and local site symmetry reduces to orthorhombic. Optical absorption spectra are recorded at room temperature. From the optical absorption study, the Racah parameters (B = 521 cm^?1, C = 2,861 cm^?1), cubic crystal field splitting parameter (Dq = 1,851 cm^?1) and nephelauxetic parameters (h = 2.06, k = 0.21) are determined. These parameters together with EPR data are used to discuss the nature of bonding in the crystal.     

Sb Magnetic Resonance as a Local Probe for the Gap Formation in the Correlated Semimetal FeSb2

We report on a comparative study of the narrow-band semimetals FeSb₂ and its structural homologue RuSb₂ by means of ^121,123Sb nuclear quadrupole (NQR) and nuclear magnetic resonance (NMR) spectroscopy. From NQR for both compounds two temperature regimes could be identified by use of ¹²³(1/T ₁) measurements. Above 40 K a conventional activated behavior (with Δ/k _B ? 400 K for FeSb₂) dominates in ¹²³(1/T ₁), whereas below 40 K in both systems an unconventional ¹²³(1/T ₁) behavior with a smooth maximum at around 10 K is observed. To analyze this behavior, we propose the presence of T-dependent in-gap states forming a narrow energy level of localized spins with S = ½ near the bottom of the conduction band. These states might have originated from an inherent Sb-deficiency in both compounds. This model enables us to fit the ¹²³(1/T ₁) data in the entire investigated temperature range (2–200 K) for FeSb₂. Ab initio band structure calculations reveal more than a factor of two larger Δ value for RuSb₂ as compared with FeSb₂. This results in dissimilar behavior of ¹²³(1/T ₁) in FeSb₂ and RuSb₂ above 40 K evidencing the inefficiency of thermal activation of electrons over the large energy gap at T ≤ 300 K in RuSb₂ and dominating of quadrupole relaxation channel in RuSb₂ in this temperature range caused by phonon relaxation involving two-phonon (Raman) scattering. In addition, extra wide range field-sweep NMR measurements are performed at various temperatures on FeSb₂ and RuSb₂. The complex broad spectra could be modeled and from the shift of the ¹²¹Sb central transition the 3d component of the shift K _3d (T) could be extracted.     

ELDOR-detected NMR at Q-Band

In recent years, electron–electron double resonance detected nuclear magnetic resonance (EDNMR) has gained considerable attention as a pulsed electron paramagnetic resonance technique to probe hyperfine interactions. Most experiments published so far were performed at W-band frequencies or higher, as at lower frequencies detection of weakly coupled low-γ nuclei is hampered by the presence of a central blind spot, which occurs at zero frequency. In this article we show that EDNMR measurements and a meaningful data analysis is indeed possible at intermediate microwave frequencies (Q-band, 34 GHz), once experimental parameters have been optimized. With highly selective detection pulses and Gaussian shaped electron–electron double resonance (ELDOR) pulses it is possible to detect low-γ nuclei coupled to paramagnetic Mn²⁺. Weakly coupled ¹⁴N resonances, which are separated from the zero frequency by only 2.8 MHz, were readily detected. In systems where different spin active nuclei are coupled to the electron spin, particular care has to be taken when using higher powered ELDOR pulses, as combination frequencies from the two nuclei (?m _S = ±1, ?m _I,1 = ±1, ?m _I,2 = ±1) can lead to severe line broadening and complicated EDNMR spectra. We also compare the EDNMR spectra of ¹³C-labeled Mn–DOTA to ¹³C-Mims electron–nuclear double resonance to get a better insight into the similarities and differences in the results of the two techniques for ¹³C hyperfine coupling.     

Simulating Suppression Effects in Pulsed ENDOR, and the ‘Hole in the Middle’ of Mims and Davies ENDOR Spectra

All pulsed electron-nuclear double resonance (ENDOR) techniques, and in particular the Mims and Davies sequences, suffer from detectability biases (‘blindspots’) that are directly correlated to the size of the hyperfine interactions of coupled nuclei. Our efforts at ENDOR ‘crystallography’ and ‘mechanism determination’ with these techniques have led our group to refine our simulations of pulsed ENDOR spectra to take into account these biases, and we here describe the process and illustrate it with several examples. We first focus on an issue whose major significance is not widely appreciated, the ‘hole in the middle’ of pulsed ENDOR spectra caused by the n = 0 suppression hole in Mims ENDOR and by the analogous A → 0 suppression in Davies ENDOR for I = ½ and for ²H (I = 1). We then discuss the general treatment of suppression effects for I = 1, illustrating it with a treatment of Mims suppression for ¹⁴N.     

One-Dimensional Ising Models with Long Range Interactions: Cluster Expansion,Phase-Separating Point

We consider the phase separation problem for the one-dimensional ferromagnetic Ising model with long-range two-body interaction, J(n) = n ^?2+α , where ${n\in {\rm {I\!N}}}$ denotes the distance of the two spins and ${\alpha \in [0,\alpha_+[}$ with α ₊ = (log 3)/(log 2) ?1. We prove that when α = 0 the localization of the phase separation fluctuates macroscopically with a non-uniform explicit limiting law, while when 0 < α < α ₊ the macroscopic fluctuations disappear and mesoscopic ones appear with a gaussian behavior when conveniently scaled. The mean magnetization profile is also given.     

Simple vibration-insensitive cavity for laser stabilization at the 10−16 level

We present the design and realization of two reference cavities for ultra-stable lasers addressing narrow transitions in mixed-species (¹¹⁵In⁺ / ¹⁷²Yb⁺) Coulomb crystals. With a simple set-up, we achieve a fractional frequency instability close to the thermal noise limit of a 12-cm-long cavity, reaching σ _y  = 4.7 × 10^?16 at 10 s with a linear drift of 53 mHz/s. We discuss the individual instability contributions and show that in a set-up with a lower thermal noise floor and vibration sensitivity, an instability of 1 × 10^?16 can be reached. To achieve this, we implement a vibration-insensitive design for a 30-cm-long cavity mounted horizontally and conduct first tests that show a sensitivity of 1.8 × 10^?11 ms^?2 to vertical accelerations. This is about a factor of 20 less than the value observed for the short cavity. Mechanical tolerances and ways to further reduce the sensitivity are discussed.     

Spectral and surface investigations of Ca2V2O7:Eu3+ nanophosphors prepared by citrate-gel combustion method: a potential red-emitting phosphor for near-UV light-emitting diodes

In the present work, red-emitting Ca₂V₂O₇:xEu³⁺ (x = 0.5–6.0 mol%) nanophosphors, in the form of powders, were synthesized by the citrate-gel combustion method using metal nitrates as precursors and citric acid as fuel. X-ray diffraction (XRD), transmission electron microscopy (TEM), scanning electron microscopy, photoluminescence (PL) and cathodoluminescence (CL) spectroscopy were used to study the structure, morphology and spectral properties of the samples. The chemical compositions and electronic states of the powders were analyzed with X-ray photoelectron spectroscopy. The average crystallite sizes estimated using the XRD data were found to be in the range of 30–45 nm, and were cross verified by TEM. The lattice parameters determined by the POWD program were approximated as a = 7.242 Å, b = 6.674 Å, c = 6.932 Å and V = 291.24 Å³, respectively. Under UV (395 nm) (PL) and electron (CL) excitation, the nanophosphors show characteristic emission from the Eu³⁺ ion (⁵D₀ → ⁷F_j, j = 1–5) with the main peaks at 612 and 616 nm. The maximum emission intensity was recorded from the sample with an Eu³⁺ concentration of 4 mol% and a critical energy distance of 19.084 Å between the donor and the acceptor. Above this concentration, there was a reduction in the intensity due to dipole–dipole induced concentration quenching effects. The potential applications of this phosphor as a high color-purity phosphor in light-emitting diodes are evaluated.     

Synthesis and Structural, Magnetic and EPR Characterization of Discrete Finite Antiferromagnetic Chains

The synthesis, magnetic and electron paramagnetic resonance (EPR) characterisation of isolated, discrete, {Cr _n ^III } antiferromagnetically coupled chain complexes is reported for n = 6 and 7. Previous studies had reported supramolecular linked {Cr _n ^III } _x species. For n = 6, the lowest lying total spin state is diamagnetic with S = 1 and 2 first and second excited states, respectively; for n = 7, the lowest lying total spin state is S = 3/2 with S = 1/2 and 5/2 first and second excited states, respectively. The zero-field splittings of these states are well defined by low-temperature, multi-frequency EPR spectroscopy.     

Multi-Frequency EPR and DC Conductivity of Itinerant Spins in Single-Wall Carbon Nanotubes

Sealed, deoxygenated single-wall carbon nanotubes show two characteristic electron paramagnetic resonance (EPR) signals at g = 2.07 and g = 2.00 in the temperature range from 300 to 50 K. Reversible interconversion between both components was observed. The large g-shift and the temperature dependence of the EPR susceptibility of the g = 2.07 signal indicate that this signal can be attributed to itinerant spins. At low temperatures only the g = 2.00 signal remained, which could be further characterized using microwave frequencies up to 320 GHz. The direct current conductivity of a partially aligned sample was also measured. The room temperature value was estimated as 0.7 (Ωcm)^?1. The observed temperature dependence can be described by assuming temperature-activated hopping in a small-gap semiconductor with an activation energy of 3.5 meV, similar to the characteristics of the previously measured 9.4 GHz microwave conductivity.